Answers
The proof that shows that ∠B ≅ ∠D by the CPCTC is explained in the table below.
What is CPCTC?CPCTC is a postulate that stands for "corresponding parts of congruent triangles are congruent". It says that if you prove that two triangles are congruent to each other, then every of their corresponding parts are congruent.
Therefore, the proof below shows how to use CPCTC to prove that ∠B ≅ ∠D.
Statement Reason
1. BC ≅ CD 1. Given
2. AC ≅ EC 2. Given
3. ∠ACB ≅ ∠ECD 3. Vertical angles theorem
4. ΔACB ≅ ΔECD 4. SAS theorem
5. ∠B ≅ ∠D 5. CPCTC
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Related Questions
Solve the system using elimination.
3x + 10y = -4
2x + 2y = 2
([?], [ ])
Answers
Answer:
Step-by-step explanation:
that normally means we want to add our subtract a certain of the 2 equations, so that we are led with one summary equation with only one variable.
the easiest way here is possibly to multiply the second equation by 5 (to get also 10y) and then subtract it from the first equation :
3x + 10y = -4
- 10x + 10y = 10
-----------------------
-7x + 0 = -14
7x = 14
x = 2
2x + 2y = 2
gives us then
2×2 + 2y = 2
4 + 2y = 2
2y = -2
y = -1
x = 2
y = -1
Answer:
x = 2
y = -1
Step-by-step explanation:
3x + 10y = -4
- 10x + 10y = 10
7x + 0 = -14
7x = 14
x = 2
2x + 2y = 2
2×2 + 2y = 2
4 + 2y = 2
2y = -2
y = -1
find the value h(-6) where h(t) = 6t-2
Answers
Answer:
Step-by-step explanation:
Quite literally you plug in -6 into t. So therefore:
h(t)=6t-2
h(-6)=6(-6)-2
h(-6)=-36-2
h(-6)=-38
-38 is your answer
h can be replaced with f and t can be replaced with x to get your standard f(x) equation if that helps you understand it better. Remember f(x) really just means the y value of the function with an input of value x. So f(x) = x is really just y=x or a linear line.
compared to smaller firms that export, larger companies tend to multiple choice systematically scan foreign markets to see where export opportunities lie. delay exporting until after their domestic market is fully saturated. be intimidated by the complexities and mechanics of exporting to foreign countries. be reactive about seeking opportunities for profitable exporting. hesitate to seek export opportunities because they do not know how big the opportunities actually are.
Answers
According to the profit point of view, compared to smaller firms that export larger companies tend to systematically scan foreign markets to see where export opportunities lie.
What does profit mean?
In math, profit means the excess of returns over expenditure in a transaction or series of transactions.
Here we have given that, compared to smaller firms that export, larger companies tend to to be what.
And for the reason more firms are not proactive is that they are unfamiliar with foreign market opportunities; they simply do not know how big the opportunities actually are or where they might lie. Simple ignorance of the potential opportunities is a huge barrier to exporting
Here we know that, smaller firms, are often intimidated by the complexities and mechanics of exporting to countries where business practices, language, culture, legal systems, and currency are very different from the home market
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Right Answers Only! thank you
Answers
Answer: A
Step-by-step explanation:
D is wrong because its saying 3 times of the flat fee of 52.5 per month.
B is wrong because it is saying 52.5$ per gigabyte
C is wrong because the total amount is not 64.2
f(x)=x²-8x³ +26x² - 88x - 111; x = −11
Answers
Answer:
14772
Step-by-step explanation:
write an expression for the sequence of operations described below. triple s, subtract u from the result, then subtract t from what you have do not simplify any part of the expression.
Answers
The expression for the sequence of operations is 3s - u - t .
In the question ,
it is given that ,
the sequence of operation is given as " triple s, subtract u from the result, then subtract t from what you have" .
we have to write an expression for the above operation ,
So ,
first step is : triple s ,
that means the expression is 3s .
next subtract u from the result , that means ⇒ 3s - u .
next we have to subtract t from what we have ,
that means ⇒ 3s - u - t .
Therefore , the final expression is 3s - u - t .
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(please explain and show work/drawing. thank you so much!) In a certain Algebra 2 class of 22 students, 5 of them
play basketball and 11 of them play baseball. There are 3
students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball
or baseball?
Answers
Answer:
59%
Step-by-step explanation:
First, let's find the number of students who play basketball but not baseball: 5 students - 3 students = <<5-3=2>>2 students
Next, let's find the number of students who play baseball but not basketball: 11 students - 3 students = <<11-3=8>>8 students
Now, let's add up the number of students who play basketball but not baseball, the number of students who play baseball but not basketball, and the number of students who play both sports to find the total number of students who play basketball or baseball: 2 students + 8 students + 3 students = <<2+8+3=13>>13 students
Finally, we can divide the total number of students who play basketball or baseball by the total number of students in the class to find the probability that a student chosen at random plays basketball or baseball: 13 students / 22 students = 0.59
Therefore, the probability that a student chosen at random from the class plays basketball or baseball is 0.59.
Answer:
13/22
Step-by-step explanation:
The class has 22 students.
5 play basketball.
11 play baseball.
3 play both.
Break down the 5 who play basketball into:
2 play only basketball
3 play both basketball and baseball
Break down the 11 who play baseball into:
8 play only baseball
3 play both basketball and baseball (These 3 are the same 3 above)
Now we have:
2 play only basketball
8 play only baseball
3 play both
This is a total of 13.
The class has 22, so 9 don't play any sport.
That means out of 22 students, 13 play either sport, and 9 play nothing.
p(basketball or baseball) = 13/22
Let X and Y be IID Unif(0, 1). Find the expected value and the standard deviation of X-Y. i.e., the distance between X and Y.
Answers
Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: [tex]$\sqrt{\frac{1}{3}}$[/tex]
Expected value:
E(X-Y)
= E(X) - E(Y)
= 0 - 0
= 0
Standard deviation:
Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2
SD(X-Y) = [tex]$\sqrt{2}$[/tex]
= [tex]$\sqrt{\frac{1}{3}}$[/tex]
The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2.
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Y^5y^5-(y^-2)^4 complete the equation
Answers
Answer: x =2, -1
Step-by-step explanation:
Alice and Bob are playing a game where in each round, each of them rolls a fair die independently. If both roll the same number, then the game is repeated. Otherwise the player with the larger number wins. Let X be the number of rounds until the game is decided.
(a) Determine the probability mass function of X.
(b) Compute E[X].
(c) Compute Probability[ Alice win].
(d) Assume that you get paid 10USD for winning in the first round, 1USD for winning in any other round, and nothing otherwise. Compute your expected winnings.
Answers
(a) The probability mass function of X will be P(X=n) = 5/(6n)
(b) E[X] =1.2
(c) Probability [ Alice win] will be =0.5
(d) The value of expected winnings will be 4.25
(a) Let 'p' represent the probability of getting the same number on both the dices on a roll of pair of die
And (1-p) = probability of not getting the same number on both the dices on a roll of pair of die
Sample space for the same number appearing on both the dices on a roll of pair of die = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
As there are a total of 36 outcomes on a roll of pair of dice,
p = 6/36 = 1/6
Let the events be defined as:
Dn : Both Alice and Bob roll the same number on the nth roll
Wn : The game is finished in the nth roll (i.e. Alice and Bob roll different numbers (as the numbers are different, one will be larger))
Then,P(W) = P(W) , n = 1,2,3,4....infinity
Wn takes place when event D takes place in the first (n-1) rolls and Event W takes place in the nth roll
[tex]$\mathrm{P}(\mathrm{W})=\sum P\left(W_n\right), \mathrm{n}=1,2,3,4 \ldots .$[/tex]. infinity
And, W_n takes place when
Event D takes place in the first (n-1) rolls and event W takes place in the [tex]$n^{\text {th }}$[/tex] roll
[tex]P\left(W_n\right)=P\left(D_1\right)^* P\left(D_2\right)^* P\left(D_3\right) \ldots . .{ }^* P\left(D_{n-1}\right) P\left(W_n\right)P\left(D_n\right)\\=(p)P\left(W_n\right)\\=(1-p)[/tex]
Implies
[tex]$$\begin{aligned}& \left.P\left(W_n\right)=(p)^{n-1}\right)^*(1-p) \\& =\left((1 / 6)^{n-1}\right)^*(1-(1 / 6)) \\& =\left((1 / 6)^{n-1}\right)^*(5 / 6) \\& =5 /\left(6^n\right)\end{aligned}$$[/tex]
(b)
[tex]$$\begin{aligned}& \mathrm{E}[\mathrm{X}]=\sum n * P(X=n), \mathrm{n}=1,2,3,4 \ldots . . \text { infinity } \\& =\sum n * \frac{5}{6^n} \\& =5 * \sum n * \frac{1}{6^n}\end{aligned}$$[/tex]
If [tex]$\mathrm{S}=\sum n * \frac{1}{6^n}$[/tex]
Then S is a sum of infinite aritho-geometric series of the form
[tex]$$\sum_{k=1}^{\mathrm{inf}} k * r^k \text {, }$$[/tex]
The sum of which is given as [tex]$S=\frac{r}{(1-r)^2}$[/tex] for 0 < r < 1
Here, r=(1 / 6)
[tex]\Rightarrow & S=\frac{\frac{1}{6}}{\left(\frac{5}{6}\right)^2} \\& =\frac{6}{25}[/tex]
E[X] = (5) x (6/25) = (6/5)= 1.2
(c) Since the dies are fair, and the outcomes are independent, the probability of each player winning is equal
Therefore,
P(Alice WIn) = P(Bob WIn) = 0.5
(d) If X represent the round in which the game ends, then the probability of us winning in that round
P(W|X=n) = 0.5*P(X=n)
= (0.5)*(5/(6n))
P(W|X=1) = (0.5)*(5/(61)) = (5/12)
P(W|X=2,3,4...) = 0.5 - P(W|X=1) = (1/2) - (5/12) = (1/12)
Leth the variable W represent the winnings
(W|X=1) = 10
(W|X=2,3,4...) = 1
E[W] = P(W|X=1)*(W|X=1) + P(W|X=2,3,4...)*(W|X=2,3,4...)
= (10 x (5/12)) + (1 x (1/12))
= (50/12) + (1/12)= (51/12)= 4.25
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8.11 a total of 725 auto-mode social/recreational trips are made from an origin (residential area) during the peak hour. a logit model estimation is made, and three factors were found to influence the destination choice: (1) population at the destination, in thousands (coefficient
Answers
Based on this information, we can estimate that a 1,000-person increase in population at the destination, an increase of 441 auto-mode social/recreational trips from the origin during the peak hour time
a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination are associated with an increase of 725 x (0.43 + (-0.07) + 0.62) = 441 auto-mode social/recreational trips from the origin during the peak hour.
1. Calculate the total increase in auto-mode social/recreational trips from the origin during the peak hour associated with a 1,000-person increase in population at the destination, a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination by multiplying the coefficients of the logit model by 725 (the total number of trips):
725 x (0.43 + (-0.07) + 0.62) = 441
2. Therefore, we can estimate that a 1,000-person increase in population at the destination, a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination are associated with an increase of 441 auto-mode social/recreational trips from the origin during the peak hour time.
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The polynomial function p(x)=x³-3 x²+x+205 has x=-5 as a root.
What are the remaining roots of p(x) ? Separate multiple answers with a comma.
Enter the factored form of p(x).
Answers
The remaining roots of p(x) is x = -5 , 4 + 5i , 4 - 5i and the factored form of p(x) = ( x + 5 ) ( x - ( 4 + 5i ) ( x - ( 4 - 5i )
Given :
The polynomial function p(x)=x³-3 x²+x+205 has x=-5 as a root.
using synthetic division :
x = -5
5 1 -3 1 205
0 5 10 55
1 2 11 260
on solving using the quadratic formula or calculator the roots are :
x = -5 , 4 + 5i , 4 - 5i
so quadratic form of p ( x ) = ( x + 5 ) ( x - ( 4 + 5i ) ( x - ( 4 - 5i )
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4) How long will Lourdes have to wait for her plant to grow a total 14 1/4 inches
Answers
Answer:
10 [tex]\frac{5}{28}[/tex] days
Step-by-step explanation:
There are a lot of places to make mistakes, but I think that I am good.
Make a proportion:
[tex]\frac{Days}{Inches}[/tex] = [tex]\frac{Days}{Inches}[/tex] Put in the three number that you know and solve for the number of days.
[tex]\frac{7\frac{13}{21} }{10\frac{2}{3} }[/tex] = [tex]\frac{x}{14\frac{1}{4} }[/tex] Cross multiply and solve for x
10 [tex]\frac{2}{3}[/tex] x = [tex]7\frac{13}{21}[/tex]([tex]14\frac{1}{4}[/tex]) Change everything into improper fractions
[tex]\frac{32}{3}[/tex]x = ([tex]\frac{160}{21}[/tex])[tex]\frac{57}{4}[/tex] I am going to cross cancel the 160 and 4 They both can be divided by 4 and I am going to cross cancel the 21 and 57. They are both divisible by 3
[tex]\frac{32}{3}[/tex] x =( [tex]\frac{40}{7}[/tex])[tex]\frac{19}{1}[/tex]
[tex]\frac{32}{3}[/tex] x = [tex]\frac{760}{7}[/tex] Multiply both sides by [tex]\frac{3}{32}[/tex]
([tex]\frac{3}{32}[/tex])[tex]\frac{32}{3}[/tex]x =([tex]\frac{3}{32}[/tex])[tex]\frac{760}{7}[/tex] I can cross cancel 32 and 760. They both can be divided by 8
x = ([tex]\frac{3}{4}[/tex])[tex]\frac{95}{7}[/tex]
x = [tex]\frac{285}{28}[/tex]
x = 10 [tex]\frac{5}{28}[/tex] Days
Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 12], whereas waiting time in the evening is uniformly distributed on [0, 14] independent of morning waiting time.(a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv'sX1, , X10and use a rule of expected value.]min(b) What is the variance of your total waiting time? (Round your answer to two decimal places.)min2(c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time − evening time. Round the variance to two decimal places.)expected value minvariance min2(d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time − evening time. Assume a week includes only Monday through Friday.)expected value minvariance min2
Answers
The total expected waiting time including the morning and the evening time is 41/3
given that your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.
Sum of both waiting times = X+Y
Where X = morning wait time is U(0.8) and
Y = evening wait time is U(0,10)
Since X and Y are independent
Var(x+y) = Var(x)+Var(y)
Var(x) = (8^2 - 0^2)/12 = 16/3
Var(Y) = (10^2 - 0^2)/12 = 25/3
Var(x+y) = 16/3 + 25/3
= (16 + 25)/3
= 41/3
Therefore, the total expected value of waiting time including the morning and the evening time is 41/3.
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7x-8y=10 and x-8y=-26 using elimination
Answers
x= 6;
y= 4.
Step-by-step explanation:1. Write the equations.[tex](1)7x-8y=10\\\\ (2)x-8y=-26\\[/tex]
2. Subtract equation 2 from equation 1.[tex](1)7x-8y=10\\-\\ (2)x-8y=-26\\--------\\\\6x+0y=36\\ \\6x=36[/tex]
3. Solve for x.[tex]\frac{6x}{6} =\frac{36}{6} \\ \\x=6[/tex]
4. Use the calculated value of "x" in any of the equation to the value of "y".For this solution, we are going to use equation 2 to get the value of "y".
[tex](6)-8y=-26\\\\-8y=-26-6\\ \\-8y=-32\\ \\\frac{-8y}{-8} =\frac{-32}{-8} \\ \\y=4[/tex]
5. Verify.If the answers are correct, both equations should return the same value in both sides of the equal (=) sign.
[tex]7(6)-8(4)=10\\ \\42-32=10\\ \\10=10[/tex]
That's correct.
[tex](6)-8(4)=-26\\ \\6-32=-26\\ \\-26=-26[/tex]
That's correct.
Hence, the answers are correct.
find the integral please
Answers
Done :) Refer to the photo taken. Let me know if this is what you where looking for. Sorry for the sideways image.
The original price of a scarf was $16, During a store closing sale, a shopper saved $12 on the scarf, What percentage discount did she receive? Explain or show your reasoning.
Answers
Answer:
The shopper received a 75% discount
Step-by-step explanation:
ok so first we turn it into an equation
let x=percentage discount
16(x)=12
x=.75
discount=75%
on my knees begging pls im tired and exhausted
A) If 3/5 of the 595 students are seventh graders, and 5/8 of them participated in the competition, about how many seventh graders participated in the competition? Describe the process you used to find your answer. (2 points)
b) If 2/5 of the 595 students are eighth graders, and 7/8 of them participated in the competition, about how many eighth graders participated in the competition? Describe the process you used to find your answer. (2 points).
c) About how many total students participated? Describe the process you used to find your answer. (2 points) Using the process shown above, I added 206 and 215 to get 421 total participants
Answers
a) The number of seventh graders that participated in the competition was of 223.
b) The number of eight graders that participated in the competition was of 208.
c) The total number of students that participated in the competition is of 431.
How to obtain the amounts?The amounts in this problem are obtained applying the proportions given by the fractions.
For item a, we have that the amount is 5/8 of 3/5 of 595, hence the total amount is obtained as follows:
5/8 x 3/5 x 595 = 223 students.(rounding to the nearest integer).
For eight graders in item b, we have that 7/8 of 2/5 of 595 students participated, hence the number of students that participated in the competition is given as follows:
7/8 x 2/5 x 595 = 208 students. (rounding to the nearest integer).
Then the total number of students that participated in the competition is given by the sum of these amounts as follows:
223 + 208 = 431 students.
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taking . definitions: a nullcline of this system is a line on which either or . more precisely, a vertical nullcline of this system is a line on which , and likewise, a horizontal nullcline of this system is a line on which . (a) write an equation for a vertical nullcline that is not a coordinate axis:
Answers
The a) equation for the vertical nullcline is y = -4x + 4 and horizontal nullcline is x = -3y + 1. The b) equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)
We have
dx/dt = x(1 - x/3 - y)
dy/dt = y(1 - y/4 - x)
a) To get the equation for vertical nullcline, not on the coordinate axis we take
dy/dt = 0
or, y(1 - y/4 - x) = 0
or, 1 - y/4 - x = 0
or, y/4 = 1 - x
or, y = -4x + 4
Similar;y for horizontal nullcline not on coordinate axis we take
dx/dt = 0
or, (1 - x/3 - y) = 0
or, x/3 = 1 - y
or, x = -3y + 1
b)
To get the equilibrium points of the nullcline system we simply take
Here the x nullcline will intersect y nullcline at
x = 0 and x = 1 - x/3 - y
y = 0 and y = 1 - y/4 - x
therefore we have equilibrium points
for x = 0 and y = 0 at(0,0)
x = 0 and y = 1 - y/4 - x at (0, 4/5)
x = 1 - x/3 - y and y = 0 at (3/4 , 0)
x = 1 - x/3 - y and y = 1 - y/4 - x at (3/8 , 1/2)
Hence the equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)
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Complete Question
(Image Attached)
How many miles is it from Austin Texas to Seattle Washington by car?
Answers
Answer:
The total driving distance from Austin, TX to Seattle, WA is 2,128 miles
Step-by-step explanation:
Answer:
i believe it is a 2,116.4 mile drive.
Step-by-step explanation:
Shaquanna kicks a football. It’s height in feet is given by h= -16t^2 + 16t where t represents the time in seconds after kick. After how many seconds does the football hit the ground?
Answers
Answer:
Step-by-step explanation:
the question is asking, or implying, when is [tex]t^{2}[/tex] = t :?
if you are thinking at 1, you're correct. so the ball will hit the ground at 1 second
Write the equation in slope-intercept form.
–2x + 4y = 12
Answers
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 2x + 4y = 12 ( add 2x to both sides )
4y = 2x + 12 ( divide through by 4 )
y = [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex] , that is
y = [tex]\frac{1}{2}[/tex] x + 3
Find axis of symmetry
Answers
Answer:
Step-by-step explanation:
x=-4
a town's population was 7500 at the beginning of the year 2000 and has been decreasing by 3.2 % each year thereafter.
Answers
Answer:
In 2022, the town's population is 2220.
Step-by-step explanation:
It currently the year 2022. Hence, 22 years have passed since 2000.
2022 − 2000 = 22
To solve for the town's population today, first multiply the years passed since 2000 by the percent decrease each year.
[tex]22 \, \textrm{years} \times \dfrac{3.2 \, \%}{\textrm{year}} = 70.4 \, \%[/tex]
Then, subtract that percent of the population in 2000 from the population in 2000.
[tex]7500-(70.4 \,\% \cdot 7500)[/tex]
[tex]= 7500 - 5280[/tex]
[tex]=2220[/tex]
James fenced in his backyard. The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide. Use the perimeter formula to find the length of his rectangular yard in inches: P = 2L + 2W. (1 foot = 12 inches)
Answers
The length of James's rectangular yard, given a fence perimeter of 20 feet and a width of 2 feet, is 8 feet, equivalent to 96 inches.
How to use the perimeter of a rectangle?Given: Perimeter (P) = 20 feet, Width (W) = 2 feet,
Conversion factor: 1 foot = 12 inches
Using the formula for perimeter: P = 2L + 2W
Substitute the given values: 20 = 2L + 2(2)
Simplify: 20 = 2L + 4
Subtract 4 from both sides: 16 = 2L
Divide by 2: L = 8 feet
Convert feet to inches: Length (in inches) = 8 feet * 12 inches/foot = 96 inches
So, the length of the rectangular yard is 96 inches.
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To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula and solve for the length in inches. The length of James' rectangular yard is 108 inches.
Explanation:To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula. However, since we need the length in inches, we will convert the feet to inches using the conversion factor of 1 foot = 12 inches.
Let's solve:
Convert the width from feet to inches: 2 feet * 12 inches/foot = 24 inchesSubstitute the values into the formula: 20 feet = 2L + 24 inchesSince the units don't match, we need to convert 20 feet to inches: 20 feet * 12 inches/foot = 240 inchesNow we have the equation: 240 inches = 2L + 24 inchesIsolate L by subtracting 24 inches from both sides: 240 inches - 24 inches = 2LSimplify: 216 inches = 2LDivide both sides by 2: 216 inches / 2 = LSolve: L = 108 inchesThe length of James' rectangular yard is 108 inches.
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3. Net income = gross profits - (cost to bring goods into store + ___)
A. long-term liabilities
B. total assets
C. operating expenses
D. cost of merchandise sold
Answers
Answer: D & C
Step-by-step explanation:
The net Income of the business is represented as
Net profits or income = Net sales revenue (gross income) – Cost of goods and services sold – Administration, operating, marketing, and advertising costs, taxes, interests, and other expenses.
Here C is an option because we need to take operating expenses into consideration but if you consider cost of goods brought into store as operating then option changes to D.
D represents the sales which helps us determine the net income of the business.
What is 1 2/3 - 5/6 ??
Answers
The Subtraction of the given fraction using the number line is 5/6.
The correct answer option is option A
How to subtract fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction while a denominator is the lower value or bottom value of a fraction.
1 2/3 - 5/6
= 5/3 - 5/6
Find the lowest common multiple of the denominators and divide
= (10-5) / 6
= 5/6
In conclusion, 5/6 is the answer to the subtraction of fraction.
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For the following exercises, express each function H as a composition of two functions F and G where H(x) = (fog)(x)
Answers
42) The functions F and G are G(x) = (2x - 1)/ (3x + 4) and F(x) = √x
43) The functions F and G are G(x) = 3x² - 4 and F(x) = 1/x⁻³.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given composite function is
H(x) = (fog)(x).
42)
H(x) =√[(2x - 1)/ (3x + 4)]
Rewrite the above equation
H(x) =√[G(x)] where G(x) = (2x - 1)/ (3x + 4)
H(x) = F(G(x)) where F(x) = √x
42)
H(x) =1/(3x² - 4)⁻³
Rewrite the above function
H(x) =1/[G(x)]⁻³ where G(x) = 1/(3x² - 4)
H(x) = F(G(x)) where F(x) = 1/x⁻³
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True or False. If a cylinder and cone
have the same height and diameter, the
volume of the cylinder will always be
greater than that of the cones.
Answers
Answer:
This statement is false
Step-by-step explanation:
This statement is false. The volume of a cylinder with a given height and diameter will always be greater than that of a cone with the same height and diameter if the base of the cone is smaller than the base of the cylinder. However, if the base of the cone is the same size as the base of the cylinder, then the volume of the cone will be equal to that of the cylinder.
A soccer coach surveyed the players to determine the number who preferred selling coupon books, magazine subscriptions, or both for their fundraiser. The results are given in the Venn diagram. To the nearest whole percent, what is the value of a in the relative frequency table for the survey results? a = 27% a = 42% a = 81% a = 88%
Answers
The value of a in the relative frequency table for the survey results a = 27%
From the given Venn diagram, the total number of players = 11 + 3 + 7 + 5 = 26
The number of players preferred magazines books which are not coupon books = 7
The relative frequency for the players who preferred magazines books which are not coupon books (a)=
magazine books but not coupon books/ total player = 7 / 26 = 0.269
In percent,
7/26 x 100 = 26.9 = 27%
Hence, a = 27%
Therefore, the value of a in the relative frequency table for the survey results a = 27%
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